What is the complexity of matrix addition?

Question

I have found some mentions in another question of matrix addition being a quadratic operation. But I think it is linear.

If I double the size of a matrix, I need to calc

Answer 1

Usually the problem is defined using square matrices "of size N", meaning NxN. By that definition, matrix addition is an O(N^2) since you must visit each of the NxN elements exactly once.

By that same definition, matrix multiplication (using square NxN matrices) is O(N^3) because you need to visit N elements in each of the source matrices to compute each of the NxN elements in the product matrix.

Generally, all matrix operations have a lower bound of O(N^2) simply because you must visit each element at least once to compute anything involving the whole matrix.